Method and apparatus for determining flow rates

ABSTRACT

A fiber optic sensor system provides sufficient thermal information to determine the mass flow rates of produced fluids within a well bore, using an optical fiber placed within or adjacent to the well bore without interference with production or prejudicing the integrity of the well. Mass flow rates of fluid in a conduit ( 20 ) located in a heat sink differing in temperature from the fluid are determined by obtaining a distributed temperature profile ( 32 ) of fluid flowing along a length of conduit ( 15 ) by using optical data obtained from a length of optical fiber in thermal contact therewith, obtaining a profile of the heat sink temperature external to the conduit, and deriving mass flow rates of fluids in the conduit from the said profiles and from measured thermal transfer parameters.

This invention relates to a method and apparatus for determining flowrates. In particular, it is concerned with the determination of the rateof flow of fluids in a conduit, using techniques for acquiring adistributed temperature profile in an optical fibre over a period oftime. Using this time-dependent temperature data, the mass flow rates offluids along the conduit can be determined when appropriate constantsare known. These constants relate to a number of parameters, of whichtime is of particular importance, and also include measures of distanceand thermal variables such as temperature, conductivity and specificheat.

Mass flow rate information is a very important tool for the efficientmanagement of oil wells and the like. It is of course important to havereliable production data, as soon as possible, not only for its ownsake. If flow rate data is promptly available, it may also be activelyused to adjust or improve the flow rates, to diagnose immediate orpotential problems, or to trigger alarms. Significant variations in flowcan be met with an appropriate management response.

It has been known in principle for over 25 years that thermal data canbe used to derive mass flow rate information, and that this informationis applicable to oil field operations and the like. Reference is made tothe paper “Use of the Temperature Log for Determining Flow Rates inProducing Wells”, Curtis M R and Witterholt E J, Society of PetroleumEngineers of AIME Paper No SPE 4637. Curtis and Wdterhoft describe amethod for calculating mass flow rate of a fluid up a well bore as afunction of the temperature profile based on algorithms developed byRamey, published as “Well-bore Heat Transmissionr”, Ramey H,J.Pet.Tech., April 1962.

Nevertheless, as a practical matter, in the economically andcommercially important field of determining the mass flow rate ofproduced or injected fluids within a well bore, downhole measurementshave typically been made using either spinner or venturi techniques inone or a plurality of locations within the production tubing. Theequipment or devices that have been used have been either permanentlyinstalled in the well bore or conveyed into a measuring location bywireline.

These currently used devices do however have well known disadvantages.The spinner device is typically run on a wireline. Use of this techniquecommonly involves shutting in the well for extended periods whilesetting up the equipment, and then running the sensor and cable in thewell, which presents a hazard to the integrity of the well. Surveys ofthis kind are carried out infrequently, and only provide aninstantaneous picture of the flow characteristics of the well.

In order to obtain continuous flow information, it is necessary to usedownhole instrumentation that is permanently installed. A particularbenefit of permanent instrumentation is that it enables a producing wellto be better controlled. Venturi techniques, in which the pressure dropacross a known orifice is measured, enable flow rates to be permanentlymonitored, but do however have limitations. Firstly, the orifice devicerestricts the internal diameter of the tubing. Secondly, the devicerelies upon two independent high accuracy pressure sensors, but theoutput of such devices has a tendency to drift with time. Thirdly, theventuri device must be routinely calibrated to a fixed fluid mixdensity, to ensure continued accuracy of measurement

For the foregoing reasons, among others, there is and has been for along time a continuing need to find and develop improved methods fordownhole mass flow rate monitoring.

We have developed sensing and measuring equipment based onopto-electronic systems at a surface location operatively connected tofibre optic sensors deployed downhole. Using such systems, it is notnecessary to have any electronics downhole and the fibre sensors canprovide temperature and pressure information, while being resistant totemperatures up to 250° C. and above.

It has been known for over 15 years that optical fibres can reporttemperature distributions. See for example GB 2122337 and EP 0213872. Wehave now found that it is possible to combine, in a useful and practicaland advantageous manner, the derivation of mass flow rates from thermaldata with the acquisition of thermal data by means of a fibre opticsensor.

Typically, the thermal data is acquired as follows. A laser light pulseis sent down an optical fibre wave guide. As the pulse of light travelsalong the wave guide, the thermal molecular vibration at each pointalong the length of the wave guide causes a very weak reflected signalto travel back up the fibre towards the source. An optical couplersplits the reflected light away from the fibre and takes it to adetector. The time lapse between the launch of the light pulse anddetection allows the distance of the reflection point down the opticalfibre to be calculated, since the speed of light in the fibre isconstant and is known. The amplitude of the returned light is a functionof the molecular vibration at the reflection point, increasing withincreasing temperature. As reflected light is detected over a timeperiod corresponding for the time taken for the light pulse to travelthe length of the optical fibre and back, the output of the detector iseffectively a distributed temperature profile along the whole length ofthe fibre.

The present invention addresses the deficiencies of the prior artmethods of determining downhole flow rates and provides methods andapparatus utilising a distributed fibre optic sensor. We have found thata single optical sensor system can provide sufficient thermalinformation to determine the mass flow rates of produced fluids within awell bore, using an optical fibre placed within or adjacent to the wellbore, almost instantaneously, at any time, substantially continuously ifrequired, without interference with production or prejudicing theintegrity of the well.

The present invention concerns aspects of the method and apparatusdescribed below. The scope of the invention extends to all novel aspectsthereof whether individually or in combination with any of the otherfeatures disclosed herein.

More specifically, in one aspect of the invention a method ofdetermining mass flow rates of fluid in a conduit located in a heat sinkdiffering in temperature from the fluid may comprise obtaining adistributed temperature profile of fluid flowing along a length ofconduit by means of optical data obtained from a length of optical fibrein thermal contact therewith, obtaining a profile of the heat sinktemperature external to the conduit, and deriving mass flow rates offluids in the conduit from the said profiles and from measured thermaltransfer parameters.

Correspondingly, apparatus for determining mass flow rates of fluid in aconduit located in a heat sink differing in temperature from the fluidmay comprise a length of optical fibre in thermal contact with thefluid, means for obtaining a distributed temperature profile of fluidflowing along a length of conduit by means of optical data obtained fromsaid length of optical fibre, and means for deriving mass flow rates offluids in the conduit from the said distributed temperature profile,from a profile of the heat sink temperature external to the conduit, andfrom measured thermal transfer parameters.

In a further aspect of the invention there is provided a method ofmonitoring the mass flow rates of fluids flowing in variable quantitiesalong a length of underground conduit, including monitoring the saidrates during both a calibration period and an observation period (whichmay include some or all of the calibration period); which methodcomprises:

(a) establishing distributed temperature measuring apparatus comprisingan optical fibre extending along the said length of conduit in thermalcontact with the fluid and/or with the conduit, together with means forpassing light along the optical fibre in the said length, receivinglight emergent therefrom, and interpreting temperature- andlocation-related characteristics of said emergent light in terms of thetemperature profile of the optical fibre at a series of locations alongthe said length of conduit;

(b) determining the natural geothermal profile along the length of theconduit to be monitored (the natural profile being the profile in theabsence of heating or cooling from the conduit);

(c) running fluid to be monitored through the said length of conduit;

(d) in the calibration period:

(i) measuring the actual mass flow rates of the fluid during time isintervals;

(ii) during those intervals, obtaining distributed temperature profilesof the length of conduit by passing light along the optical fibre andinterpreting temperature- and location-related characteristics of lightemergent from the said length;

(iii) correlating the distributed temperature profiles observed in (i)with the flow rates measured in (ii) whereby to obtain calibration data,and especially time-dependent parameters, which calibrate thetemperature measuring apparatus in terms of mass flow rate;

(e) in the observation period: monitoring the distributed temperatureprofile of the length of conduit by means of the distributed temperaturemeasuring apparatus and obtaining therefrom the flow rates of the fluidin the length of conduit using the calibration data obtained in thecalibration period.

Correspondingly, apparatus for monitoring the mass flow rates of fluidsflowing in variable quantities along a length of underground conduit maycomprise:

(a) distributed temperature measuring apparatus comprising an opticalfibre extending along the said length of conduit in thermal contact withthe fluid and/or with the conduit, together with means for passing lightalong the optical fibre in the said length, receiving light emergenttherefrom and interpreting temperature- and location-relatedcharacteristics of said emergent light in terms of the temperatureprofile of the optical fibre at a series of locations along the saidlength of conduit;

(b) means for determining the natural geothermal profile along thelength of the conduit to be monitored (the natural profile being theprofile in the absence of heating or cooling from the conduit);

(c) optionally, means for measuring the actual mass flow rates of thefluid during time intervals in a calibration period;

(d) means for correlating distributed temperature profiles obtained from(a) with actual flow rates whereby to obtain calibration data whichcalibrate the temperature measuring apparatus in terms of mass flowrate;

(e) means for monitoring the distributed temperature profile of thelength of conduit by means of the distributed temperature measuringapparatus and obtaining therefrom the flow rates of the fluid in thelength of conduit using the calibration data obtained from (d).

Although the method and apparatus of the invention as set out aboverelate to the use of a temperature profile along a length of conduit, itis theoretically possible to obtain effective data from measurements ata single location. As a practical matter, it is believed thatmeasurements at a plurality of locations along the conduit aredesirable, because the results are not then so critically dependent uponone set of data. If the same mass flow rate is measured at severallocations, especially in an underground borehole, an average result isobtained which is less influenced by local variations from idealbehaviour.

The most preferred methods involve making a plurality of measurements ateach of a plurality of locations in the conduit.

Various preferred and optional features of the invention will becomeapparent from the following description. Details of method steps orapparatus elements that are individually known in oilfield and relatedscience and technology are not given, as they will be well known tothose skilled in these arts. Thus, to take just one example, thedetermination of geothermal gradient may be accomplished by anyconventional or novel means and is not further discussed herein.

In an embodiment of the invention, a fibre optic distributed temperaturesensor is installed in a well bore inside a thermally conductive tubewhich is suitably clamped or bonded to a substantial continuous fixedstructure extending over the length of well bore in which the opticalfibre is operatively deployed. Suitably, the fixed structure may be theconduit for the fluid whose mass flow rate is to be measured. Thisconduit may be the oil well casing, or the production tubing, or anyother similar conduit appropriate to the particular downhole environmentwhere the flow rate is required to be known.

The tube may be filled with thermally conductive liquid, to ensurefunctional thermal contact between the optical fibre and the conduitconcerned, and preferably between the fibre and the fluid whose flowrate is to be determined.

The mass flow rate of the fluid is determined by the application ofpredetermined algorithms to the distributed temperature profile that isdetermined for the fluid. Typical applications of the invention are thecalculation of mass flow rate in producing oil, water and gas wells, ina variety of different fluid combinations, and in injecting water wells.

Among the different possible methods of determining mass flow rate fromtemperature, two are preferred in the practice of the present invention.

In a first preferred method, flow rate data is derived from the thermalbehaviour of fluids flowing through massive underground formations,which act as heat sinks at their natural temperatures. By ‘naturaltemperatures’ we mean their temperatures in the absence of any flow ofheating or cooling fluid through the conduit that runs through theseformations. Generally speaking, in a vertical well, the temperaturerises more or less linearly with depth, and it is normally sufficientlyaccurate for the purposes of the present invention to treat theresulting geothermal gradient as being linear. As fluid flows along theconduit it is heated or cooled by conduction. The temperature at anypoint depends on the thermal properties of the flowing fluid, of theinstalled completion (the production tubing and associated hardwarewithin the lined well bore of a well, including such equipment asdown-hole safety valves, packers and circulating valves) and of thesurrounding formation, and is dependent upon flow rate, pressure,volume, temperature (PVT), Joule-Thompson effects, and frictionallosses, and can be time dependent.

It is observed that, starting from a point of interest deep within thewell, which may be a point at which fluid in temperature equilibriumwith the surrounding formation is introduced into the well bore, thetemperature profile of the fluid above that point (as the fluid flowsupwards through a heat sink of progressively lower temperature) takesthe form of a curve which approaches an asymptote to a straight lineparallel to the geothermal profile, ie of the same geothermal gradientbut displaced by a certain temperature. The actual shape of theasymptotic curve is determined by the thermal properties of the system,mass flow rates, friction, Joule-Thompson and PVT properties of theflowing fluid as has been described in publications such as Curtis andWitterholt, SPE 4637, mentioned above, to which reference should be madefor further details.

Appropriate algorithms for this first preferred method are:

T(z,t)=T _(ge) +G _(g) z−G _(g) A+(T _(fe) −T _(ge) +G _(g) A)e ^(−z/A)

where

A=Qρ _(f) C _(f)(k _(h) +r _(cl) Uf(t))/2πr _(cl) Uk _(h)

and

f(t)=−In(r _(ce)/2(κt)^(0.5)−0.29

and

G_(g)=Geothermal gradient

T_(ge)=Geothermal temperature at depth of fluid entry

T_(fe)=Fluid entry temperature

Z=distance from entry zone

Q=Mass flow rate

ρ_(f)=Fluid density

C_(f)=Fluid specific heat

k_(h)=formal thermal conductivity

U=Overall heat transfer coefficient

t=Flowing time

r_(cl)=Inner radius of casing

r_(ce)=Outer radius of casing

κ=Thermal diffusivity of casing

Equivalent algorithms exist for calculating the flow rate of fluid beinginjected into an underground reservoir. See for example the paper“Temperature Logging in Injection Wells”, Witterholt E J and Tixier M P,SPE 4022. Similarly, for gas production, see for example the paper“Temperature Surveys in Gas Producing Wells”, by Tixier M P and Kunz KS, AIME Annual Meeting, Chicago 1955. These algorithms may be improvedby taking into account the effective heating due to flowing frictionpressure drop. Additionally, changes in pressure, volume and temperatureproperties up the well may be taken into account by the use of computernodal analysis. Suitable commercially available temperature modellingsoftware includes that sold by Landmark under the trade name WellCat.

During the calibration period, the algorithms are used while the actualfluid flow rate is determined independently, so that the flow ratebecomes a known value. The known flow rate, whether a flow rate of fluidproduced from the well or a flow rate of fluid injected into the well,is compared with the measured temperature profile of the length ofconduit in consideration, as a function of producing time and depth. Thecomparison may be optimised by modification of the formula constantssuch as fluid specific heat (C_(f)), the thermal conductivity of thesurrounding rock formation (k_(h)), the overall heat transfercoefficient (U) and the thermal diffusivity of the casing (κ), which arespecific to a particular well completion, a particular formation, andparticular fluid properties. In effect, the calibration phase in whichthe actual flow rates are known enables the constants in the algorithmsto be established for a particular well. A more accurate analysis may beobtained by calculating the formula constants themselves, by employing aleast squares regression fit of the predicted data to the measured dataas a function of time and depth and flow rate.

The actual algorithms to be used may be chosen at will. An algorithm maybe based on the theoretical models described here, optionally modifiedto fit the observed temperatures and flow rates during the calibrationstage, or it may be derived entirely empirically, by a curve-fittingexercise. Thus, a set of observations may be made on an actual well, andan equation may be constructed, using those parameters that appear to besignificant, that adequately fits the observed results.

Once the constants in the algorithms have been derived as a function ofknown flow rates during the calibration period, it is possible tocalculate the flow rate in an observation period using the same derivedconstants. Normally, the observation period will follow the calibrationperiod, and this is of course essential if real time data is required.It would however be possible to use an observation period before acalibration period, if it would be acceptable to derive only historicdata.

A second preferred method for deriving mass flow rates from temperaturedata occurs where the temperature of the flowing fluid changes as aresult of a change, typically a loss, of pressure. This may be due to adiscontinuous change in the size or type of conduit, for example a 3½″to 4½″ (89 mm to 114 mm) crossover, or at a tubing shoe or the like, ora loss of pressure along a horizontal length of production conduit. Thetemperature changes can be related, by the use of appropriate equations,to the flow rate of the fluid. Again, parameters that are fixed asconstants in a particular downhole environment are the thermalproperties of the flowing fluid, of the installed completion and of thesurrounding formation. Dynamic properties of the fluid such as its JouleThompson and PVT characteristics should also be taken into account.

When this approach is followed, the temperature profile at a change inflowing cross section of the conduit is characterised by either anincrease or a decrease in temperature. The mass flow rate of the fluidcan be determined, as before, from an analysis of the time baseddistributed temperature profile over the length of conduit concerned,where the PVT characteristics of the flowing fluid are known and theother relevant constants are derived from measurements made during thecalibration period when the flow rates are known.

The algorithms defining the relationship between the temperatureprofile, the length of the conduit being investigated, and time, withrespect to the thermal properties of the flowing fluid and thesurroundings, are available from published literature describing heattransfer in pipelines. Reference is made in particular to two books:

1 Hein, Michael A. “HP 41 Pipeline Hydraulics and Heat TransferPrograms”, Pemwell books, 1984, ISDN 0878 14 255X

2 Carslaw, H. S. and Jaeger, J. C. “Conducdion of Heat in Solids”,Clarendon Press, 2^(nd) Edition, 1959.

The invention is illustrated diagrammatically by way of example in theaccompanying drawings, in which:

FIG. 1 illustrates on the left hand side a cross section of a producingoil well, and on the right hand side a graph of temperature (abscissa)against height/depth (ordinate), the depth scale being indicated by thecorresponding location in the adjacent depicted well bore; and

FIG. 2 is a graph of the fluid temperature at a given location in thewell, plotted (as ordinate) against time (abscissa), illustrating theeffects of changes in mass flow rate.

In FIG. 1, the oil well is shown with a casing 11 extending from theground surface 12 into and through a producing reservoir 13. Productiontubing 15 extends inside the casing from the usual oil flow controlapparatus 16 located above ground at the wellhead and terminates insidethe casing at a depth D above a producing zone 17. The upper boundary ofthe producing zone is marked by a closure 18 which holds the lower endof the production tubing in place within the casing.

In accordance with the invention, an optical fibre is deployed withinthe well in a suitable duct, such as optical fibre deployment tube 20,which is a continuous tube having two limbs, in effect a U-tube,beginning and ending in connection with surface mounted instrumentation22, including a light source (a laser), a light detector, and dataprocessing apparatus, which respectively act as means for passing lightalong the optical fibre, means for receiving returning light emergenttherefrom, and means for interpreting temperature- and location-relatedcharacteristics of said emergent light in terms of the temperatureprofile of the optical fibre at a series of locations along the fibresensor deployed in the well. The deployment tube extends from theinstrumentation down the well between the production tubing and thecasing, through closure 18 and through the producing zone 17, returningby the same route. The tube is thermally conductive, and will typicallybe clamped to the outside of the production tubing, in good thermalcontact therewith, but may alternatively be installed on the oil wellcasing, if fluid temperatures in the annulus between tubing and casingare to be measured.

The instrumentation 22 may comprise commercially availableinstrumentation, such as the model DTS-800 made by York Sensors Ltd ofChandlers Ford, Hampshire, England. The optical fibre within tube 20 isdesirably coated to withstand the high temperatures and corrosive fluidsencountered in a downhole environment. Typically, the fibre willcomprise an inner core or wave guide of about 50 μm diameter surroundedby a lower refractive index cladding, total diameter about 125 μm. Thecladding may be coated with a sealing layer that is impervious todownhole fluids, and finally an abrasion resistant coating to bring thetotal diameter of the fibre up to about 155-400 μm.

Such a fibre can be deployed in the deployment tube 20 by hydraulicmeans, and can correspondingly be replaced if necessary. The hydraulicdeployment fluid remains in the tube after deployment of the fibre andprovides a thermal bridge to the tube wall, so that the optical fibre isin thermal contact with the fluids whose mass flow rates are to bemeasured, in the conduit comprised of the production tubing and the wellcasing.

With appropriate instrumentation, temperatures can be measured from −40°C. to +300° C., with an accuracy of 0.5° or better. The temperaturemeasurements are absolute rather than relative, do not drift and do notneed calibration against any reference. In practical terms, theinformation can be obtained continuously, meaning as frequently as every7 seconds. This is the practical minimum time needed at present tocollect sufficient reflected light from the length of the fibre. Themeasurements can be repeated immediately or after any suitable timeinterval. In a production well, monitoring may be carried out hourly ordaily, according to operating requirements.

Locations along the conduit may be distinguished at intervals of 1 malong the fibre, for a fibre length of up to 10 km. In a 40 km fibre,temperature readings at 10 m intervals are considered, for practicalpurposes, to be continuous over the length of the fibre.

The graphical right hand side of FIG. 1 illustrates the measuredtemperature profiles. The natural geothermal profile 30 is a straightline relation between depth and temperature. It is derived from simpletemperature measurements, by conventional apparatus, at differentdepths. Deviations from a straight line, due to varying thermalconductivities in the surrounding formation, are considered to be sominor as to be insignificant for the purposes of the invention, inalmost all cases.

The heavier curve 32 represents the distributed temperature profile overthe whole well. It coincides with the geothermal profile below thereservoir 13, where there is no flow, and the fluid is at equilibriumwith its surroundings. As fluid enters the well from the reservoir andrises in the producing zone 17, it passes into cooler regions and beginsto lose heat to the surrounding formations, which act as a heat sink ata temperature related to depth by the geothermal profile. Depending onflow rates, conductivities and the like, the temperature of the fluidrising in the well falls.

At depth D, the diameter of the conduit, constituted by the casing 11 inthe producing zone 17 and by the tubing 15 above depth D, is suddenlyreduced. As illustrated, the fluid temperature drops sharply at point 36as it enters the narrower bore of the production tubing. Thereafter, therising fluid continues to show a temperature differential to thesurrounding formation, and the relation between its temperature and itsdepth approaches the asymptote 34 which is a straight line at thegeothermal gradient, displaced from the geothermal profile 30 by thedifference in temperature between the temperature of fluid rising in asteady state from an indefinitely deep well and the temperature of thesurrounding rock.

FIG. 2 shows a temperature curve 40 plotted against elapsed time at agiven location along the deployment tube 20 above reservoir 13. At thestart time t₀, there is no fluid flow, and the measured temperature Thas equalised with the geothermal temperature T_(ge), which isrepresented as a horizontal line Q₀, denoting a flow rate (Q) of zero.

At time t₀, fluid begins to flow upwards at a first intermediate flowrate Q_(B), and the measured temperature T rises exponentially as warmerfluid rises to the measuring point from lower down the well. As thisfluid rises, it loses heat to the surrounding heat sink and thetemperature rises on curve Q_(B). After time t₁, the flow increases to ahigher rate Q_(C), whereupon the measured temperature increases fasterand curve 40 approaches the curve Q_(C). At time t₂, curve 40 is forpractical purposes aligned with Q_(C), which it then follows until timet₃, when there is a sharp fall to a low flow rate Q_(A). The measuredtemperature T then falls between times t₃ and t₄, after which it risesagain with the corresponding curve Q_(A), which it follows until timet₅, and continues to follow until the flow rate changes again.

In accordance with the invention, the flow rates Q_(A), Q_(B), and Q_(C)are measured by other means during the calibration stage, which allowsan appropriate equation to be sufficiently accurately derived frommeasurements made during the time intervals t₀ to t₁, t₂ to t₃, and t₄to t₅. After the calibration stage, when the measurements are madesubsequently, the various flow rates Q can then be monitored. It can bedetermined when the new curve is reached, because the observedtemperature change rates then fit the equation.

At any given location, the curves are in practice not smooth, due tolocal perturbations. By taking the measurements at a range of locationsalong the a length of the conduit where flow rates are constant (that isto say, a constant diameter conduit and no inflow of fluid from thesurrounding formation), the data can be averaged to give reliableresults. If fluid does enter the conduit at a certain depth, separatesets of measurements above and below the inflow will show the rate atwhich new fluid adds to the flow, by simple difference. A suitablelength of conduit over which measurements need to be made to give areliable result is around 100 m.

The distributed temperature profile curves 32, 40, provide the basis forthe derivation of the required mass flow rates, as described. The methodand apparatus are calibrated by measurements made at a time when massflow rates are determined independently by conventional means, such asby spinner or venturi methods. Data processing in the instrumentation 22provides real time information which is invaluable in managing the oilwell. The novel application of thermal analytical techniques totemperature data derived from optical fibre distributed temperaturesensors, in accordance with this invention, enables accurate,substantially non-intrusive, and easily replaceable downhole apparatusto give continuous real-time mass flow data. This in turn can be used inmany ways, as well known in the art, to enhance oil well management.

What is claimed is:
 1. A method of determining mass flow rates of fluid in a conduit located in a heat sink differing in temperature from the fluid, comprising obtaining a distributed temperature profile of fluid flowing along a length of conduit by means of optical data obtained from a length of optical fibre in thermal contact therewith; obtaining a profile of the heat sink temperature external to the conduit; and deriving mass flow rates of fluids in the conduit from the said profiles and from measured thermal transfer parameters.
 2. A method of monitoring the mass flow rates of fluids flowing in variable quantities along a length of underground conduit, including monitoring the said rates during both a calibration period and an observation period (which may include some or all of the calibration period); which method comprises: (a) establishing distributed temperature measuring apparatus comprising an optical fibre extending along the said length of conduit in thermal contact with the fluid and/or with the conduit, together with means for passing light along the optical fibre in the said length, receiving light emergent therefrom, and interpreting temperature- and location-related characteristics of said emergent light in terms of the temperature profile of the optical fibre at a series of locations along the said length of conduit; (b) determining the natural geothermal profile along the length of the conduit to be monitored; (c) running fluid to be monitored through the said length of conduit; (d) in the calibration period: (i) measuring the actual mass flow rates of the fluid during time intervals; (ii) during those intervals, obtaining distributed temperature profiles of the length of conduit by passing light along the optical fibre and interpreting temperature- and location-related characteristics of light emergent from the said length; (iii) correlating the distributed temperature profiles observed in (i) with the flow rates measured in (ii) whereby to obtain calibration data which calibrate the temperature measuring apparatus in terms of mass flow rate; (e) in the observation period: monitoring the distributed temperature profile of the length of conduit by means of the distributed temperature measuring apparatus and obtaining therefrom the flow rates of the fluid in the length of conduit using the calibration data obtained in the calibration period.
 3. A method according to claim 1 wherein the fluid is oil, water or gas from an underground reservoir and the conduit is a production conduit for extracting said fluid from a producing well for the same.
 4. A method according to claim 1 wherein flow rate data is derived from the thermal behaviour of the fluid flowing through a massive underground formation, which acts as a heat sink at its natural temperature.
 5. A method according to claim 4 including the step of deriving the mass flow rate of the fluid from the formula: T(z,t)=T _(ge) +G _(g) z−G _(g) A+(T _(fe) −T _(ge) +G _(g) A)e ^(−z/A) where A=Qρ _(f) C _(f)(k _(h) +r _(cl) Uf(t))/2πr _(cl) Uk _(h) and f(t)=−In(r _(ce)/2(κt)^(0.5)−0.29 and G_(g)=Geothermal gradient T_(ge)=Geothermal temperature at depth of fluid entry T_(fe)=Fluid entry temperature Z=distance from entry zone Q=Mass flow rate ρ_(f)=Fluid density C_(f)=Fluid specific heat k_(h)=formal thermal conductivity U=Overall heat transfer coefficient t=Flowing time r_(cl)=Inner radius of casing r_(ce)=Outer radius of casing κ=Thermal diffusivity of casing.
 6. A method according to claim 1 including the step of deriving the mass flow rates from temperature data obtained where the temperature of the flowing fluid changes as a result of a change of pressure.
 7. A method according to claim 1 which comprises determining the temperature of the fluid at a plurality of locations from 1 m to 10 m apart in the length of conduit.
 8. Apparatus for determining mass flow rates of fluid in a conduit located in a heat sink differing in temperature from the fluid, comprising: a length of optical fibre in thermal contact with the fluid; means for obtaining a distributed temperature profile of fluid flowing along a length of conduit by means of optical data obtained from said length of optical fibre; and means for deriving mass flow rates of fluids in the conduit from the said distributed temperature profile, from a profile of the heat sink temperature external to the conduit, and from measured thermal transfer parameters.
 9. Apparatus for monitoring the mass flow rates of fluids flowing in variable quantities along a length of underground conduit, comprising: (a) distributed temperature measuring apparatus comprising an optical fibre extending along the said length of conduit in thermal contact with the fluid and/or with the conduit, together with means for passing light along the optical fibre in the said length, receiving light emergent therefrom and interpreting temperature- and location-related characteristics of said emergent light in terms of the temperature profile of the optical fibre at a series of locations along the said length of conduit; (b) means for determining the natural geothermal profile along the length of the conduit to be monitored; (c) optionally, means for measuring the actual mass flow rates of the fluid during time intervals in a calibration period; (d) means for correlating distributed temperature profiles obtained from (a) with actual flow rates whereby to obtain calibration data which calibrate the temperature measuring apparatus in terms of mass flow rate; (e) means for monitoring the distributed temperature profile of the length of conduit by means of the distributed temperature measuring apparatus and obtaining therefrom the flow rates of the fluid in the length of conduit using the calibration data obtained from (d).
 10. Apparatus according to claim 8 wherein the optical fibre is installed in a well bore inside a thermally conductive tube which is clamped or bonded to a substantial continuous fixed structure extending over the length of well bore in which the optical fibre is operatively deployed.
 11. Apparatus according to claim 10 wherein the fixed structure is the conduit for the fluid whose mass flow rate is to be measured.
 12. Apparatus according to claim 10 wherein the tube is filled with thermally conductive liquid. 